Robust estimation of a high-dimensional integrated covariance matrix
Robust estimation of a high-dimensional integrated covariance matrix
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高维积分协方差矩阵的鲁棒估计
DOI：
10.1080/03610918.2014.991038
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Takayuki MORIMOTO and Shuichi NAGATA
中科院分区：
文献类型：
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作者：
森本 孝之;川崎 能典;Takayuki MORIMOTO and Yoshinori KAWASAKI;森本 孝之;Takayuki MORIMOTO and Shuichi NAGATA
在这篇文章中，我们考虑了一个鲁棒的方法来估计已实现的协方差矩阵计算为日内高频收益率的叉积之和。根据金融计量经济学最近的文章，已实现协方差矩阵基本上被市场微观结构噪声污染了。虽然自21世纪初以来，已经研究了从矩阵中去除噪声的技术，但他们主要研究了具有统计显著样本量的低维协方差矩阵。我们专注于噪声鲁棒协方差估计在匡威的情况下，即，一个高维的协方差矩阵可能与一个小的样本容量。对于估计，我们利用基于协方差矩阵的最大特征值渐近遵循Tracy-Widom分布的特性的统计假设检验。零假设假定对数收益率不是纯噪声。如果样本特征值大于相关临界值，则我们无法拒绝零假设。仿真结果表明，这里研究的估计器性能优于其他衡量的均方误差。实证分析表明，我们提出的估计可以采用预测未来的协方差矩阵使用真实的数据。
In this article, we consider a robust method of estimating a realized covariance matrix calculated as the sum of cross products of intraday high-frequency returns. According to recent articles in financial econometrics, the realized covariance matrix is essentially contaminated with market microstructure noise. Although techniques for removing noise from the matrix have been studied since the early 2000s, they have primarily investigated a low-dimensional covariance matrix with statistically significant sample sizes. We focus on noise-robust covariance estimation under converse circumstances, that is, a high-dimensional covariance matrix possibly with a small sample size. For the estimation, we utilize a statistical hypothesis test based on the characteristic that the largest eigenvalue of the covariance matrix asymptotically follows a Tracy–Widom distribution. The null hypothesis assumes that log returns are not pure noises. If a sample eigenvalue is larger than the relevant critical value, then we fail to reject the null hypothesis. The simulation results show that the estimator studied here performs better than others as measured by mean squared error. The empirical analysis shows that our proposed estimator can be adopted to forecast future covariance matrices using real data.